On April 14, 1963, The Beatles first saw The Rolling Stones performing in London's Crawdaddy Club, packed with screaming girls dancing on tabletops.

"It was a match made in heaven, rampant youth colliding," wrote Andrew Loog Oldham, the Stones' first manager and now a Sirius XM deejay, in his 1998 memoir. The lads stayed up until 4 a.m. together. George Harrison lobbied Decca -- still trying to live down the humiliation of spurning the Beatles in 1962 -- to sign the Stones, and Oldham landed the deal. "If Decca's doorman started whistling, they would have signed him," he said.

Frantic to find a song for his new charges, the manager ran into John Lennon and Paul McCartney exiting a taxi, and they gave the Stones "I Wanna Be Your Man" (inferior to their hit "I Want to Hold Your Hand"). Released by the Stones in November 1963, it hit No. 12 on the British charts, marking the beginning of the bands' benevolent rivalry.

Soon, McCartney turned Jagger on to pot. When a stoned Jagger and Brian Jones sang backup on 1966's "Yellow Submarine," Lennon nearly electrocuted himself by immersing a 240-volt microphone wrapped in a condom in water for the gurgling sound.

In 1968, Lennon performed with Keith Richards in the film The Rolling Stones Rock and Roll Circus, in which Lennon joshes Jagger, "Those were the days -- 'I Wanna Hold Your Man.' " The Stones honored those days by opening their 50th anniversary concert in 2012 with their only Beatles song.